Abstract |
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Admissible reductions - i. e. reduction obtained through sufficient or ancillarity σ-fields - are analyzed in the case of a sequential Bayesian experiment. These reductions are analyzed both in the model generating n observations and in the model generating the nth observation given observations up to the (n-1)th one. This leads to so-called initially and sequentially admissible reductions. It is then Shown why it may be useful, for inference and for prediction purposes, to construct reduction which are both initially and sequentially admissible. The concept of transitivity is shown to arise in a natural way when investigating under what conditions is a sequentially admissible reduction also initially admissible. This condition of transitivity is also shown to be necessary in the sense of being imlplied by a reduction both initially and sequentially admissible. Finally, this concept of transitivity is related to the "concept of non-causality" as introduced in the econometric literature. Particular attention is paid to admissible reduction obtained through cuts. |